This code will update an item setting the date and the person when it was deactivated (please be aware here that we set the time like this 'DateTime.Now', the time from the web server when the code is executed)

But at the same time, we have a store procedure which updates the item and that store procedure sets also the DeactivateDt

Honestly, it should not matter whether you update the date from app tier or db tier. It could be business requirement also. However maintaining consistency across the application is more important from standardization & auditing point of view. This standardization would help in auditing the application in future, in case of any issues.

However, under this circumstances, given a chance, I would recommend DB layer to update the date automatically with default value as GETDATE(), when a new record is inserted.

Again to maintain consistency while updating, if your requirement is to set the same date to all, you can do something like as follows: